The alternate inventory, or "apoc mode", being based on X-Com Apocalypse's way of equipping with gear tied to soldiers instead of craft, is an acquired taste. I've found it highly useful for the high equipment turnover of lategame mission and for preventing craft pile bloat, but I'll be the first to admit it requires some getting used to.
If it's not to your liking, you can always turn it off, as previously suggested.
Regarding inventory management, there's a few tools with limited documentation you might find helpful:
-A useful tool to migrate to a new transport, or to quickly load and unload craft equipment for missions that limit available gear, like mansions, is craft save/load. Press F5 in the craft equipment screen to save your stashed gear to up to 10 different templates, F9 to load. This is a good way to switch from and to diving or space gear. In Apoc mode, this is mostly useful for setting up a stockpile of backup gear and supplies.
-If you have a preferred loadout for a specific soldier, you can save a personal loadout to S, and L to load it. Personal loadout includes both armor and equipment. Another useful thing to switch back your gals to their normal gear after an undersea adventure
-You can also use up to 20 preconfigured templates, F5 to save and F9 to load in the soldier inventory screen, to quickly switch to a pre-selected choice of gear, and optionally, armor. The 1-0 keys can quickly load templates 1 through 10, press 1-10 twice to access templates 11 through 20
